## Electronic Journal of Probability

### On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries

#### Abstract

In the first part of the article we prove limit theorems of Marchenko-Pastur type for the average spectral distribution of random matrices with dependent entries satisfying a weak law of large numbers, uniform bounds on moments and a martingale like condition investigated previously by Goetze and Tikhomirov. Examples include log-concave unconditional distributions on the space of matrices. In the second part we specialize to random matrices with independent isotropic unconditional log-concave rows for which (using the Tao-Vu replacement principle) we prove the circular law.

#### Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 37, 1065-1095.

Dates
Accepted: 2 June 2011
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464820206

Digital Object Identifier
doi:10.1214/EJP.v16-899

Mathematical Reviews number (MathSciNet)
MR2820070

Zentralblatt MATH identifier
1221.15049

Subjects
Primary: 15B52: Random matrices

Rights

#### Citation

Adamczak, Radoslaw. On the Marchenko-Pastur and Circular Laws for some Classes of Random Matrices with Dependent Entries. Electron. J. Probab. 16 (2011), paper no. 37, 1065--1095. doi:10.1214/EJP.v16-899. https://projecteuclid.org/euclid.ejp/1464820206

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